Mesh problem when smoothing intersecting cylinder in object
The faces with 4+ sides are called Ngons.

Ngons are not easy to handle with subdivision surfaces. They don't give predictable results, you cannot easly controle them.

You can:


Change your topology by converting all ngons and tris to quads, as they have user-easily-predictable results with subsurf, but you must do it manually and it will take lot of time.
Convert ngons to tris, by triangulating and splitting your geometry (expecially concaves faces). This can be done automatically with the given commands with good results, but in will not be subsurfaced as percfectly as it would be done with only quads and will be hard to do further modeling onto.
Don't use subsurface to smooth edges but bevel them (manually or with the modifier)